The vertex is a minimum. This is because the a value is 1, which is positive. Anytime the a value is positive, the parabola opens up, creating a minimum value. The opposite is true for a negative a value.
The domain is all real numbers. This is the case for all quadratic functions.
The range is y≥2. As stated before, it has a minimum so all y values must be higher than that of the minimum.